More on the connectivity of convex sets
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- by D. S. Bridges PDF
- Proc. Amer. Math. Soc. 68 (1978), 214-216 Request permission
Abstract:
This note, written from a constructive viewpoint, shows how Mandelker’s results on connectivity of compact intervals [3] extend to open balls in Banach space, and complete, convex subsets of arbitrary normed spaces. This is achieved by proving the equivalence of Mandelker’s notion of connectivity with one of those discussed in [2].References
- Errett Bishop, Foundations of constructive analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221878
- Douglas S. Bridges, On the connectivity of convex sets, Bull. London Math. Soc. 10 (1978), no. 1, 86–90. MR 478008, DOI 10.1112/blms/10.1.86
- Mark Mandelker, Connectivity of an interval, Proc. Amer. Math. Soc. 54 (1976), 170–172. MR 390140, DOI 10.1090/S0002-9939-1976-0390140-4
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 214-216
- MSC: Primary 03F65; Secondary 46B05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0480195-2
- MathSciNet review: 480195